Elliptic curve isogeny class 578.1-b over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-578.1-b
• Conductor: 578.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{2}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 2 \); class number \(1\).

Elliptic curves in class 578.1-b over \(\Q(\sqrt{2}) \)

Isogeny class 578.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
578.1-b1	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -19 a - 33\) , \( 26 a + 35\bigr] \)
578.1-b2	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -9 a - 13\) , \( -22 a - 29\bigr] \)
578.1-b3	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -464 a - 1273\) , \( -10018 a - 19601\bigr] \)
578.1-b4	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 445 a - 685\) , \( 6530 a - 9359\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph